Natalie,
This is kind of strange that an insurance company cancels an insurance policy because information regarding your previous insurance company was not obtained and no letters were sent to inform you of the cancellation. Having said this, if the insurance company did send out letters concerning your policy and it's likely cancellation, then they must have a record of it somewhere on their system even if the letters didn't reach you. So you can ask to see the reminders from your current insurance company and if they fail to provide you with this, then they obviously did not send anything out. I'm not sure about the independent company you're referring to but I'm sure the Citizen Advice Bureau can help you with that.